Abstract
In this paper, a class of new KKM theorem is obtained which unifies and improves the corresponding results in [2], [3], [6], [7], [11]. As applications, we utilize our result to obtain some matching theorem, coincidence theorem, fixed point theorem, minimax inequality theorem and section theorem.
Similar content being viewed by others
References
C., Bardaro and R., Ceppitelli, Some further generalization of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities, J. Math. Anal. Appl., 132 (1988), 484–490.
Chang, Shihsen and Zhang, Ying, Generalized KKM theorem and variational inequalities. J. Math. Anal. Appl., 159 (1991), 208–223.
Chang, Shihsen and Ma, Yihai, Generalized KKM theorem on H-space with applications, J. Math. Anal. Appl., 163 (1992), 406–421.
Chang, Shihsen, Variational Inequality and Complementarity Problem Theory with Applications, Shanghai Sci. and Tech. Literature Publishing House, Shanghai (1991). (in Chinese)
Ky, Fan, Some properties of convex sets related to fixed point theorems, Math. Ann., 266 (1984), 519–537.
Ky, Fan, A generalization of Tychonoff's fixed point theorems, Math. Ann., 42 (1961), 303–310.
C. Horvath, Some results on multi-valued mappings and inequalities without convexity, in “Nonlinear and Convex Analysis”, Lecture Notes in Pure and Appl. Math. Ser. V. 107 Springer Verlag, (1987).
W. K., Kim, Some applications of the Kakutani fixed point theorem, J. Math. Anal. Appl., 121 (1987). 119–122.
B., Knaster, B., Kuratowski and S., Mazurkiewicz, Ein beweis des fixpunktsatzas fur n-dimensionale simplexe, Fund. Math., 14 (1929), 132–137.
M., Lassonde, On the use of KKM multifunctions in fixed point theory and related topic. J. Math. Anal. Appl., 97 (1983), 151–201.
S., Park, Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl., 141 (1989), 164–176.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Shisheng, Z., Xian, Z. On a class of new KKM theorem with applications. Appl Math Mech 17, 819–826 (1996). https://doi.org/10.1007/BF00127181
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00127181